Zhang Kai, Yang Zhesen, Fang Chen
Beijing National Laboratory for Condensed Matter Physics, and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China.
University of Chinese Academy of Sciences, Beijing 100049, China.
Phys Rev Lett. 2020 Sep 18;125(12):126402. doi: 10.1103/PhysRevLett.125.126402.
We establish exact relations between the winding of "energy" (eigenvalue of Hamiltonian) on the complex plane as momentum traverses the Brillouin zone with periodic boundary condition, and the presence of "skin modes" with open boundary conditions in non-Hermitian systems. We show that the nonzero winding with respect to any complex reference energy leads to the presence of skin modes, and vice versa. We also show that both the nonzero winding and the presence of skin modes share the common physical origin that is the nonvanishing current through the system.
我们建立了在具有周期性边界条件下动量遍历布里渊区时，复平面上“能量”（哈密顿量的本征值）的缠绕数与非厄米系统中开放边界条件下“趋肤模式”的存在之间的确切关系。我们表明，相对于任何复参考能量的非零缠绕数会导致趋肤模式的出现，反之亦然。我们还表明，非零缠绕数和趋肤模式的出现都有共同的物理起源，即通过系统的非零电流。
